The result stretched United's winless league run to three games and left them five points behind leaders Chelsea ahead of a tough fixture list, starting with Wednesday's Champions League clash with Italian side Atalanta at Old Trafford.
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"Everyone is sad, everyone is with their head down at the moment," Matic told the club's official website on Sunday.
"It's time to stick together, to analyse this game as soon as possible, then to think about the next one, which is in three or four days against a very good side, Atalanta.
"It's also going to be hard. We are very disappointed, but I think that, in the future, we will show we are much better than this.
"Every next game is the most important, every next game is a new challenge, an opportunity to show your qualities. We're going to take responsibility. We're going to step up and see what we can do. I'm sure that we can do a lot."
Matic also apologised to United fans for the team's shambolic performance against Leicester.
"We are sorry for them," he added. "They support us, especially away and they are top. They deserve much, much better than this."